This review describes in detail the essential techniques used in microscopic theories on spintronics. We have investigated the domain wall dynamics induced by electric current based on the $s$-$d$ exchange model. The domain wall is treated as rigid and planar and is described by two collective coordinates: the position and angle of wall magnetization. The effect of conduction electrons on the domain wall dynamics is calculated in the case of slowly varying spin structure (close to the adiabatic limit) by use of a gauge transformation. The spin-transfer torque and force on the wall are expressed by Feynman diagrams and calculated systematically using non-equilibrium Green's functions, treating electrons fully quantum mechanically. The wall dynamics is discussed based on two coupled equations of motion derived for two collective coordinates. The force is related to electron transport properties, resistivity, and the Hall effect. Effect of conduction electron spin relaxation on the torque and wall dynamics is also studied.Comment: manucript accepted to Phys. Re

Effects of conduction electrons on magnetization dynamics, represented by spin torques, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called $\beta$-term and the Gilbert damping, $\alpha$, in the presence of electrons' spin-relaxation processes, which are modeled by quenched magnetic (and spin-orbit) impurities. The obtained results such as $\alpha \ne \beta$ hold for localized as well as itinerant ferromagnetism.Comment: 4 page

The dynamics of magnetostatically coupled vortices in two nanodisks is here investigated analytically and numerically. The rigid vortex model is employed to calculate the magnetostatic interaction between the nanodisks. We use Thiele's equation where collective degrees of freedom describe the motion of each vortex core. We find that there are eigenfrequencies of circular vortex core motion around the disk center, which depend on the core polarizations of the vortices. We also obtain the energy absorption rate of the system when subjected to an oscillating in-plane magnetic field. Finally, we can draw an analogy between this vortex system and a van der Waals diatomic molecule.

Large spin current applied to a uniform ferromagnet leads to a spin-wave instability as pointed out recently. In this paper, it is shown that such spin-wave instability is absent in a state containing a domain wall, which indicates that nucleation of magnetic domains occurs above a certain critical spin current. This scenario is supported also by an explicit energy comparison of the two states under spin current.PACS numbers: 72.25. Ba, 75.40.Gb Magnetization dynamics driven by spin torque from a spin polarized current (spin current) has been studied extensively after the theoretical prediction [1, 2] that a spin current can be used to flip the magnetization in pillar (or spin valve) structures [3,4,5,6,7,8]. As a theoretical framework to describe such current-induced magnetization dynamics, Bazaliy, Jones and Zhang (BJZ) [9] derived a modified Landau-Lifshitz-Gilbert (LLG) equation for a fully-polarized ferromagnet (half metal) with a new term proportional to j · ∇n. This new term represents a spin torque that a current of density j exerts on a local magnetization n. Later on, it was generalized to the partially polarized case with an interpretation of j as the spin current density, j s [10,11]. In the Hamiltonian, the effect of spin torque appears in a formwhere θ and φ are polar angles which parameterize n. As seen from this form, spin current favors a magnetic configuration with spatial gradient, or more precisely, with finite Berry-phase curvature. It is thus expected that a large spin current destabilizes a uniform ferromagnetic state. This is indeed seen from the spin-wave energy [9,10,11],where λ = J/K and κ = K ⊥ /K, with J, K and K ⊥ being exchange constant, easy-and hard-axis anisotropy constants, respectively, of localized spins. The first term is the well-known spin-wave dispersion with anisotropy gap. becomes negative for a range of k. This means that there exist states with negative excitation energy, indicating the instability of the assumed uniformlymagnetized state [9,10,11]. The true ground state under spin current, however, remains to be identified.In this Letter, we point out that possible ground state is a state containing domain walls. Namely, the energy of a domain wall becomes lower than the uniform ferromagnetic state when a spin current exceeds a certain critical value j cr s . The behavior of nucleated domains depends much on the magnetic anisotropy parameters; Flowing domain wall is stable when the anisotropy is of uniaxial type. For the case of large hard-axis anisotropy, static domain wall is stable at the nucleation threshold, but when it starts to flow under larger current, even a state with a domain wall becomes unstable. The nature of the resulting state is still unknown.Our prediction of domain formation by spin current may be related to the very recent experimental observations in metallic and semiconducting pillars and films [12,13,14,15,16,17], which suggest spatially inhomogeneous magnetization reversal. Domain nucleation is also suggested by recent numerical simulation...